1.Logic   
∃   there exist 
∀   for all 
p⇒q   p implies q / if p, then q 
p⇔q   p if and only if q /p is equivalent to q / p and q are equivalent 
2.Sets   
x∈A   x belongs to A / x is an element (or a member) of A 
x∉A   x does not belong to A / x is not an element (or a member) of A 
A⊂B   A is contained in B / A is a subset of B 
A⊃B   A contains B / B is a subset of A 
A∩B   A cap B / A meet B / A intersection B 
A∪B   A cup B / A join B / A union B 
A\B   A minus B / the diference between A and B 
A×B   A cross B / the cartesian product of A and B 
3. Real numbers   
x+1   x plus one 
x-1   x minus one 
x±1   x plus or minus one 
xy   xy / x multiplied by y 
  
(x - y)(x + y)   x minus y, x plus y 
  
x y   x over y 
=   the equals sign 
x = 5   x equals 5 / x is equal to 5 
x≠5   x (is) not equal to 5 
x≡y   x is equivalent to (or identical with) y 
x ≡ y   x is not equivalent to (or identical with) y 
x > y   x is greater than y 
x≥y   x is greater than or equal to y 
x < y   x is less than y 
x≤y   x is less than or equal to y 
0 < x < 1   zero is less than x is less than 1 
0≤x≤1   zero is less than or equal to x is less than or equal to 1 
| x |   mod x / modulus x 
x 2   x squared / x (raised) to the power 2 
x 3   x cubed 
x 4   x to the fourth / x to the power four 
x n   x to the nth / x to the power n 
x −n   x to the (power) minus n 
x   (square) root x / the square root of x 
x 3   cube root (of) x 
x 4   fourth root (of) x 
x n   nth root (of) x 
( x+y ) 2   x plus y all squared 
( x y ) 2   x over y all squared 
n!   n factorial 
x ^   x hat 
x ¯   x bar 
x ˜   x tilde 
x i   xi / x subscript i / x suffix i / x sub i 
∑ i=1 n a i   the sum from i equals one to n a i / the sum as i runs from 1 to n of the a i 
4. Linear algebra   
‖ x ‖   the norm (or modulus) of x 
OA →   OA / vector OA 
OA ¯   OA / the length of the segment OA 
A T   A transpose / the transpose of A 
A −1   A inverse / the inverse of A 
5. Functions   
f( x )   fx / f of x / the function f of x 
f:S→T   a function f from S to T 
x→y   x maps to y / x is sent (or mapped) to y 
f'( x )   f prime x / f dash x / the (first) derivative of f with respect to x 
f''( x )   f double-prime x / f double-dash x / the second derivative of f with respect to x 
f'''( x )   triple-prime x / f triple-dash x / the third derivative of f with respect to x 
f (4) ( x )   f four x / the fourth derivative of f with respect to x 
∂f ∂ x 1   the partial (derivative) of f with respect to x1 
∂ 2 f ∂ x 1 2   the second partial (derivative) of f with respect to x1 
∫ 0 ∞   the integral from zero to infinity 
lim⁡ x→0   the limit as x approaches zero 
lim⁡ x→ 0 +   the limit as x approaches zero from above 
lim⁡ x→ 0 −   the limit as x approaches zero from below 
log e y   log y to the base e / log to the base e of y / natural log (of) y 
ln⁡y   log y to the base e / log to the base e of y / natural log (of) y